How the MBK scheme is different from the others

The MBK pseudopotential [6] is a norm-conserving version of the Vanderbilt's ultrasoft pseudopotential [10]. The feature allows us to take multiple states with the same angular momentum quantum number into account for construction of a separable pseudopotential. Thus, it is guranteed that the MBK scheme is more accurate than the other schemes when semi-core states are included in the construction of pseudopotential. When the MBK scheme is used, one must care the reference energy given by the fifth column in the specification by the keyword, pseudo.NandL. Generally, the energy of zero is a good starting point for further trial and error. Since in the MBK scheme the number of projectors in the separable form is determined by the number of states with the same angular momentum quantum number, the number of projectors can be different from each other depending on the choice of valence states. Also, it should be noted that even if the MBK scheme is employed by the keyword, vps.type, the TM scheme is employed for angular momentum quantum number with only one state, and the number of projectors is determined by the keyword, Blochl.projector.num for the separable pseudopotential with the angular momentum quantum number.